关于Menger PN-空间中增算子不动点的研究

On Fixed Points for Increasing Operators in Menger PN-Spaces

首先在 Menger PN-空间中引入锥理论 ,然后利用锥理论来讨论 Menger PN-空间的增算子不动点问题 ,证明了 1正规锥中 ,凝聚增算子存在不动点 ;2正则锥中 ,连续增算子存在不动点 ;3强极小锥中 ,增算子存在不动点。文章的结果不仅推广了 Banach空间的相应结果 ,也丰富了 Menger PN-空间中的理论。

In this article, the concept of cone in Menger PN-spaces is introduced, then by using this concept, the existence of the fixed point for an increasing operator in Menger PN-spaces is discussed. And we verify that: ①there exist fixed points for the condensing and increasing operators in normed cone;②there exist fixed points for the continuous increasing operators in regular cone;③there exist fixed points for the increasing operators in strong minimal cone. The results not only generalize the corresponding results in Banach spaces, but also enrich the theory of Menger PN-spaces.